Coevolutionary arms races between prey defense and predator offense — the Red Queen hypothesis. Populations evolve in trait space; a mutation in one species drives selection in the other.
Red Queen hypothesis (Van Valen 1973): Organisms must constantly evolve just to maintain fitness relative to co-evolving adversaries. Formalized by matching allele models and Hamiltonian dynamics in trait space.
Model: Prey have defense trait d, predators have offense trait a. Prey fitness ∝ max(0, d−a); predator fitness ∝ max(0, a−d). Each generation, selection + mutation shifts trait distributions. The system evolves forever — there is no stable equilibrium.